Problem: $g(n) = -7n^{3}+6n^{2}+5n-3(f(n))$ $f(x) = -4x+4$ $ f(g(2)) = {?} $
Explanation: First, let's solve for the value of the inner function, $g(2)$ . Then we'll know what to plug into the outer function. $g(2) = -7(2^{3})+6(2^{2})+(5)(2)-3(f(2))$ To solve for the value of $g$ , we need to solve for the value of $f(2)$ $f(2) = (-4)(2)+4$ $f(2) = -4$ That means $g(2) = -7(2^{3})+6(2^{2})+(5)(2)+(-3)(-4)$ $g(2) = -10$ Now we know that $g(2) = -10$ . Let's solve for $f(g(2))$ , which is $f(-10)$ $f(-10) = (-4)(-10)+4$ $f(-10) = 44$